Distributed Linear Estimation Via a Roaming Token

We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate, and jumps from one agent to another in its vicinity according to the probabilities of a Markov chain. When the token is at an agent it records the agent's local information. We analyze the proposed algorithm and show that it is consistent and asymptotically optimal, in the sense that its mean-square-error (MSE) rate of decay approaches the centralized one as the number of iterations increases. We show these results for a scenario where the network changes over time, and we consider two different sets of assumptions on the network instantiations: (I) they are i.i.d. and connected on the average, or (II) that they are deterministic and strongly connected for every finite time window of a fixed size. Simulations show our algorithm is competitive with consensus+innovations and diffusion type of algorithms, achieving a smaller MSE at each iteration in all considered scenarios.